My research focuses on the properties of solutions to singular stochastic (partial) differential equations, such as their Markovian semi-group, or their local times. These questions arise in the study of scaling limit of various discrete models such as wetting models, and a major challenge is to understand these properties in the light of the new tools provided by regularity structures and rough path techniques.
My PhD, which I defended in April 2019 under the supervision of Lorenzo Zambotti at Sorbonne Université in Paris, concerns a family of stochastic PDEs which arise as infinite-dimensional analogs of Bessel processes.
List of Publications:
H. Elad Altman (2020): Integration by Parts Formulae for the Laws of Bessel Bridges via Hypergeometric Functions, Electronic Communications in Probability, Volume 25, https://projecteuclid.org/euclid.ecp/1593569166
Jean-Dominique Deuschel, Henri Elad Altman, Tal Orenshtein (2019): On the gradient dynamics associated with wetting models, arXiv preprint 1908.08850
H. Elad Altman (2019): Bessel SPDEs with general Dirichlet boundary conditions, arXiv preprint 1908.02241
H. Elad Altman and L. Zambotti (2018): Bessel SPDEs and renormalised local times, Probability Theory and Related Fields (2019). https://doi.org/10.1007/s00440-019-00926-0
H. Elad Altman (2018): Bismut-Elworthy-Li Formulae for Bessel Processes, Séminaire de Probabilités XLIX 2018 - Springer
PhD thesis: thesis_revised
Elad Altman H, Zambotti L, 2020, Bessel SPDEs and renormalised local times, Probability Theory and Related Fields, Vol:176, ISSN:0178-8051, Pages:757-807
Elad Altman H, 2018, Bismut-Elworthy-Li formulae for Bessel processes, Lecture Notes in Mathematics, Vol:2215, ISSN:0075-8434, Pages:183-220